Hepatitis E virus (HEV) is endemic in several developing countries of Africa and Asia. It mainly causes self-limiting waterborne infections, in either sporadic or outbreak form. Recently, HEV was shown to cause chronic infections in immunosuppressed individuals. Ribavirin and interferon, the current off-label treatment options for hepatitis E, have several side effects. Hence, there is a need for new drugs. We evaluated the antimalarial drug artesunate (ART) against genotype 1 HEV (HEV-1) and HEV-3 using a virus-replicon-based cell culture system. ART exhibited 59% and 43% inhibition of HEV-1 and HEV-3, respectively, at the highest nontoxic concentration. Computational molecular docking analysis showed that ART can bind to the helicase active site (affinity score, -7.4 kcal/mol), indicating its potential to affect ATP hydrolysis activity. An in vitro ATPase activity assay of the helicase indeed showed 24% and 55% inhibition at 19.5 µM (EC50) and 78 µM concentrations of ART, respectively. Since ATP is a substrate of RNA-dependent RNA polymerase (RdRp) as well, we evaluated the effect of ART on the enzymatic activity of the viral polymerase. Interestingly, ART showed 26% and 40% inhibition of the RdRp polymerase activity at 19.5 µM and 78 µM concentrations of ART, respectively. It could be concluded from these findings that ART inhibited replication of both HEV-1 and HEV-3 by directly targeting the activities of the viral enzymes helicase and RdRp. Considering that ART is known to be safe in pregnant women, we think this antimalarial drug deserves further evaluation in animal models.